Issqrt 5arationalnumber? Choices: (A)yes (B)no

Define rational number: Step 1: Define a rational number. A rational number can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero. Nature of sqrt(5): Step 2: Consider the nature of sqrt(5). sqrt(5) is the number which when multiplied by itself gives 5. This number cannot be expressed as a simple fraction of two integers. Check decimal representation: Step 3: Check if sqrt(5) can be a terminating or repeating decimal. Since sqrt(5) cannot be expressed as a fraction of two integers, it does not have a decimal representation that is either terminating or repeating. Conclude irrationality: Step 4: Conclude if sqrt(5) is rational or irrational. Based on the properties of rational numbers and the nature of sqrt(5), it is clear that sqrt(5) is an irrational number.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Is $\sqrt{5}$ a rational number? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

View step-by-step help

Home

Math Problems

Grade 8

Identify rational and irrational numbers

Full solution

Q. Is

\sqrt{5}

a rational number?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Define rational number: Step $1$ : Define a rational number. $\newline$ A rational number can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero.
Nature of $\sqrt{5}$ : Step $2$ : Consider the nature of $\sqrt{5}$ . $\newline$ $\sqrt{5}$ is the number which when multiplied by itself gives $5$ . This number cannot be expressed as a simple fraction of two integers.
Check decimal representation: Step $3$ : Check if $\sqrt{5}$ can be a terminating or repeating decimal. $\newline$ Since $\sqrt{5}$ cannot be expressed as a fraction of two integers, it does not have a decimal representation that is either terminating or repeating.
Conclude irrationality: Step $4$ : Conclude if $\sqrt{5}$ is rational or irrational. $\newline$ Based on the properties of rational numbers and the nature of $\sqrt{5}$ , it is clear that $\sqrt{5}$ is an irrational number.